{"paper":{"title":"Partial character tables for $\\mathbb{Z}_\\ell$-spetses","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"Gunter Malle, Jason Semeraro, Radha Kessar","submitted_at":"2025-07-11T11:24:38Z","abstract_excerpt":"Let ${\\mathbb{G}}$ be a simply connected ${\\mathbb{Z}}_\\ell$-spets, let $q$ be a prime power, prime to $\\ell$ and let $S$ be the underlying Sylow $\\ell$-subgroup. Firstly, motivated by known formulae for values of Deligne-Lusztig characters of finite reductive groups, we propose a formula for the values of the unipotent characters of ${\\mathbb{G}}(q)$ on the elements of $S$. Using this, we explicitly list the unipotent character values of the ${\\mathbb{Z}}_2$-spets $G_{24}(q)$ related to the Benson-Solomon fusion system Sol$(q)$.\n  Secondly, when $\\ell > 2$ is a very good prime for ${\\mathbb{G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08502","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.08502/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}